Looking at we can see that the first term is and the last term is where the coefficients are 5 and -11 respectively.
Now multiply the first coefficient 5 and the last coefficient -11 to get -55. Now what two numbers multiply to -55 and add to the middle coefficient -6? Let's list all of the factors of -55:
Factors of -55:
1,5,11,55
-1,-5,-11,-55 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -55
(1)*(-55)
(5)*(-11)
(-1)*(55)
(-5)*(11)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6
First Number
Second Number
Sum
1
-55
1+(-55)=-54
5
-11
5+(-11)=-6
-1
55
-1+55=54
-5
11
-5+11=6
From this list we can see that 5 and -11 add up to -6 and multiply to -55
Now looking at the expression , replace with (notice adds up to . So it is equivalent to )
Now let's factor by grouping:
Group like terms
Factor out the GCF of out of the first group. Factor out the GCF of out of the second group
Since we have a common term of , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
(